f
free loop
Type of mathematical object
EntityQ2015432
- Subclass of
Overview
All data
4 statements · 25% with external sources · numbers in brackets are citations
On other databases
2 identifiers linking free loop across the web's reference databases
Type of mathematical object
4 statements · 25% with external sources · numbers in brackets are citations
2 identifiers linking free loop across the web's reference databases
From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0
In the mathematical field of topology, a free loop is a variant of the notion of a loop. Whereas a loop has a distinguished point on it, called its basepoint, a free loop lacks such a distinguished point. Formally, let be a topological space. Then a free loop in is an equivalence class of continuous functions from the circle to . Two loops are equivalent if they differ by a reparameterization of the circle. That is, if there exists a homeomorphism such that